# week 05 APT - Risk Risk and Return Arbitrage Pricing and...

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isk and Return Risk and Return Arbitrage Pricing and

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Last Time ± The CAPM ² Critical assumptions laim ² Claim ² Implications s a stock’s contribution to/share of market risk ± β as a stock s contribution to/share of market risk ± CML and SML pplications and extensions ± Applications and extensions ± Empirical tests Week 5 FINS5513 2
Today ± Multi-index models ± Arbitrage and arbitrage pricing ² The factor model ² The pricing equation n xample ² An example Week 5 FINS5513 3

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Multi-Index Models ± In general, r i –r f = α i + Σ j β i,j (F j –r f ) + e i where F j is the jth factor/index that impacts r i , e i is the firm-specific effect for stock i, therefore Cov(e i ,e j ) = 0 for i j, Cov(e i , F j ) = 0 for all i & j. ± Alternatively r i = E(r i ) + Σ j β i,j f j + e i here f the surprise of the jth factor with E(f = 0 where f j is the surprise of the jth factor with E(f j ) 0 ± β i,j is the factor loading of asset i on factor j. indicates how sensitive asset i is to changes in factor j ² It indicates how sensitive asset i is to changes in factor j. ² Alternatively, it represents the risk exposure of asset i to ctor j Week 5 FINS5513 4 factor j.
Conditional Expectation ± A stock has expected return = 14%. ± Two factors: industrial production (IP) and interest rate (IR) ² E(IP) = 4%, E(IR) = 6% actor loadings: 15 - 4 ² Factor loadings: β IP = 1.5, β IR = 0.4 ² Actual IP = 5%, IR = 7% ² f = 1%, f = 1% IP IR ² Conditional expectation: E(r i | f IP , f IR ) = 14%+1.5 × 1%-0.4 × 1% = 15.1% Week 5 FINS5513 5

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Risk Decomposition ± The total risk of stock i is σ i 2 = Σ Σ k β i j β i k σ k + σ i 2 (e) j ,j , j, ± The first component, Σ j Σ k β i,j β i,k σ j,k , is the systematic sk associated with factor movements. risk associated with factor movements. ± The second component, σ i 2 (e), is the firm specific sk risk. ± If the factors are independent, then σ i 2 = Σ j β i,j 2 σ j 2 + σ i 2 (e) Week 5 FINS5513 6
Risk Factors ± Chen, Roll, and Ross (1986) ² Growth rate of industrial production hange in expected inflation ² Change in expected inflation ² Change in unexpected inflation ² (Yield of long-term corp bonds) – (Yield of long-term T- (g p) bonds) ² (Yield of long-term T-bonds) – (Yield of T-bills) ± Fama and French (1992) ² Market risk premium (r M –r f ) eturn of small stocks) eturn of large stocks) ² (Return of small stocks) – (Return of large stocks) ² (Return of high book-to-market stocks) – (Return of low book-to-market stocks) Week 5 FINS5513 7

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## This note was uploaded on 01/24/2011 for the course FINS 5513 taught by Professor Wangjianxin during the Three '10 term at University of New South Wales.

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week 05 APT - Risk Risk and Return Arbitrage Pricing and...

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